Posted by Anonymous on Wednesday, April 18, 2012 at 11:54am.
Does cos(1/x^2) diverge?

Math  Steve, Wednesday, April 18, 2012 at 11:56am
near x=0, yes. It oscillates faster and faster, and does not converge to any single value. In any interval (0,x) it assumes all values between 1 and 1.